Question

The length and area of cross section of a conductor are doubled, then its resistance is
A. halved
B. unchanged
C. doubled
D. quadrupled

Answer 1

Hint:The resistance of a conductor depends on the material of the conductor, the length of which the current flowing in the conductor and the area of cross section through which the current flows. Use the formula for the resistance of a conductor.

Formula used:
$R=\rho \dfrac{l}{A}$

Complete step by step answer:
A conductor is a substance that conducts electricity. This means that it allows current to pass through it. However, every conductor does not allow charges to flow through it easily and opposes the flow of current flowing through it. This opposing nature of the conductor is understood by a term called resistance of the conductor.

The resistance of a conductor depends on the material of the conductor, the length of which is flowing in the conductor and the area of cross section through which the current flows.The resistance of a conductor is given as $R=\rho \dfrac{l}{A}$ , where $\rho $ is the resistivity of the material, l is the length and A area of the cross section of the conductor.

It is given that the length and area of the cross section of the conductor is doubled. This means that the new length and cross sectional area are 2l and 2A respectively. Therefore, the new resistance of the conductor is equal to $R'=\rho \dfrac{2l}{2A}=\rho \dfrac{l}{A}$.If we compare the values of R and R’, then we understand that the resistance of the conductor is unchanged when its length and area of cross section are doubled.

Hence, the correct option is B.

Note:With this question, we can understand that until the ratio of the length to the area of the cross section of the conductor remains the same, the resistance of the conductor remains the same. Note that $l$ is the length along which the current flows and $A$ is the cross section through which the current flows.